A Borel-Weil theorem for the quantum Grassmannians

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Authors	CAROTENUTO Alessandro MROZINSKI Colin BUACHALLA Réamonn Ó.
Year of publication	2023
Type	Article in Periodical
Magazine / Source	Documenta Mathematica
MU Faculty or unit	Faculty of Science
Citation
Web	https://doi.org/10.4171/dm/913
Doi	http://dx.doi.org/10.4171/DM/913
Keywords	Quantum groups; noncommutative geometry; quantum flag manifolds; complex geometry
Description	We establish a noncommutative generalisation of the Borel–Weil theorem for the celebrated Heckenberger–Kolb calculi of the quantum Grassmannians. The result is formulated in the framework of quantum principal bundles and noncommutative complex structures, and generalises previous work of a number of authors on quantum projective space. As a direct consequence we get a novel noncommutative differential geometric presentation of the twisted Grassmannian coordinate ring studied in noncommutative projective geometry. A number of applications to the noncommutative Kähler geometry of the quantum Grassmannians are also given.
Related projects:	Homotopické a homologické metody a nástroje úzce související s matematickou fyzikou